Parameterizing Spatial Models of Infectious Disease Transmission that Incorporate Infection Time Uncertainty Using Sampling-Based Likelihood Approximations

A class of discrete-time models of infectious disease spread, referred to as individual-level models (ILMs), are typically fitted in a Bayesian Markov chain Monte Carlo (MCMC) framework. These models quantify probabilistic outcomes regarding the risk of infection of susceptible individuals due to various susceptibility and transmissibility factors, including their spatial distance from infectious individuals. The infectious pressure from infected individuals exerted on susceptible individuals is intrinsic to these ILMs. Unfortunately, quantifying this infectious pressure for data sets containing many individuals can be computationally burdensome, leading to a time-consuming likelihood calculation and, thus, computationally prohibitive MCMC-based analysis. This problem worsens when using data augmentation to allow for uncertainty in infection times. In this paper, we develop sampling methods that can be used to calculate a fast, approximate likelihood when fitting such disease models. A simple random sampling approach is initially considered followed by various spatially-stratified schemes. We test and compare the performance of our methods with both simulated data and data from the 2001 foot-and-mouth disease (FMD) epidemic in the U.K. Our results indicate that substantial computation savings can be obtained—albeit, of course, with some information loss—suggesting that such techniques may be of use in the analysis of very large epidemic data sets.一类以个体为研究对象的传染病传播离散时间模型，即个体层面模型（ILMs），通常采用贝叶斯马尔可夫链蒙特卡洛（MCMC）框架进行拟合。这类模型可量化易感个体因各类易感性与传播性因素（包括与传染源的空间距离）导致的感染风险相关概率性结果。传染源对易感个体施加的感染压力是此类个体层面模型的固有考量要素。然而，当数据集包含大量个体时，量化此类感染压力往往计算负担沉重，会导致似然计算耗时过长，进而使得基于MCMC的分析在计算上难以实现。若采用数据增强以处理感染时间的不确定性，该问题会进一步恶化。本文提出了可在拟合此类传染病模型时实现快速近似似然计算的采样方法：首先考量简单随机采样策略，随后引入多种空间分层采样方案。我们通过模拟数据与2001年英国口蹄疫（FMD）疫情的真实数据集，对本文所提方法的性能进行测试与对比。结果表明，尽管不可避免会带来一定程度的信息损失，但该方法可实现显著的计算成本节约，这提示此类技术可应用于超大规模疫情数据集的分析工作。